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Prize crossnumber, Issue 11

Our original prize crossnumber is featured on pages 56 and 57 of Issue 11.

Rules

  • Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
  • One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
  • To enter, enter the sum of the across clues below by 3 September 2020. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 October 2020.

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Dear Dirichlet, Issue 11

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

Dear Dirichlet,

You’ll be pleased to hear I’ve just finished my PhD in abstract algebra, but now I’m stressed about jobs. I need to write this grant application for a big postdoc position studying a set combined with two binary operations, but all I want to do is curl up and read my favourite book: JRR Tolkein’s The Two Towers. What should I do?

— Elven Safety, Birmingham

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Kepler’s barrels

Kepler went out shopping for a barrel full of wine,
He had a problem with the price the merchant would assign,
The merchant used a measure stick to calculate the price,
Into the barrel it did drop,
  Through a hole at centre top,
  And down and left until it stopped,
He thought it imprecise.

He said there’d be a certain price for a barrel short and fat,
And another that was tall and thin would cost the same as that,
But while the short fat barrel would hold lots and lots of wine,
The tall thin one would hold much less,
  This observation caused distress,
  Kepler started to obsess,
He didn’t think it fine.

Though Kepler paid the merchant then, he never could forget,
That inconsistent pricing, well, it really made him fret,
Day after day he pondered as he went about his work,
He just had to investigate,
  The fairness of the merchant’s rate,
  He could no more procrastinate,
Or he would go berserk.

For any given pricing, how much wine could one consume?
What measurement of barrel gave the maximum volume?
He noted that a cylinder was almost the same shape,
As the barrel he’d been using,
  For his celebratory boozing,
  And so he began his musing,
He could approximate.

For cylinders of different heights he worked out the diameter,
Assuming that the merchant’s measure was a fixed parameter,
Trying different values gave a groundbreaking conclusion,
Diameter, times by root 2,
  Would give the perfect height value,
  A maxed-out volume would ensue,
It was no illusion.

Then Kepler found out something new that really made him cheer,
All of Austria’s barrels had this ratio, or near,
So the barrel that he’d purchased had a fair price after all,
A few might slightly deviate,
  But Kepler could appreciate,
  The volume change that this creates,
Is imperceptible.

But the story doesn’t end here, because Kepler’s observation,
That the points around the max have but a tiny deviation,
Inspired Fermat’s theorem about stationary points,
It might not seem so obvious,
  But this led on to calculus,
  A field meritorious,
That never disappoints.

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Prize crossnumber, Issue 10

Our original prize crossnumber is featured on pages 48 and 49 of Issue 10.

Rules

  • Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
  • One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
  • To enter, enter the sum of the across clues below by 2 February 2020. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 14 March 2020.

Correction: Clue 13A has been corrected to “49A reversed” instead of “49D reversed”.
Correction: Clue 38D has been corrected to “33A less than 39D” instead of “33A less than 39A”.
Clarificiation: The triangle in 6D is a right-angled triangle.
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Dear Dirichlet, Issue 10

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

Dear Dirichlet,

Boy, am I in a world of woes! In the coming months, I have to go into surgery six times for a whole host of illnesses. To its credit, the hospital has allowed me to arrange my own schedule. In your doctoral opinion, which procedures should I undergo first?

— Under the weather, Cambridge

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Prize crossnumber, Issue 09

Our original prize crossnumber is featured on pages 54 and 55 of Issue 09.

Rules

  • Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
  • One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
  • To enter, enter the sum of the across clues below by 9 September 2019. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 28 September 2019.

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Dear Dirichlet, Issue 09

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

Dear Dirichlet,

My husband and I have found ourselves in a long-distance relationship. His company offered him a large promotion if he moved to Canada for six months, but it seems now that the position will require more time. I’m not sure that I want to move out there with him, or that I could be happy knowing he had to move back here. Conversation with the time difference is hard as well. Any tips?

— Getting tensor, Four Oaks

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